Hi,
The first event I ever competed in a time trial was with EMRA at LimeRock late in the fall of 2000. My main objective then was to get some track time. Although they were friendly and professional, I didn't care for the format of the event. They had you run individually for times (2 laps) and it took all afternoon for everyone to finish. The awards ceremony was dragged out as well and compared to other clubs I've run with since then, I didn't feel I got the best bang for the buck. EMRA does also run a race group which might be a better deal, but it wasn't something I was ready for at that time.
For non-competitive track time I have had very good experiences with PDA, SCDA, and the Connecticut Valley Chapter of the BMW Club (you don't have to own or run a BMW, just join). There are also other groups such as Trackmasters that have an excellent reputation in this area.
For competition ViperDays is King! Either time trials (Michelin Challenge Series) or the Viper Racing League wheel to wheel event will get you more track time, instruction and experience than anything I have found.
Good luck - I hope this helps.